Flippin' Flywheels

[MrVibrating]

Something else to try:


- for a given RPM, 'edge speed' of a disc squares with radius

- maybe some kind of radial transmission line can connect a mechanism in this outer, higher speed frame, with an inner, lower speed mechanism. A 'transmission' circumvents the need to move actual masses between these frames, while by virtue of both rotating at the same RPM, but at different actual velocities, energy from the inner mechanism might 'step' - almost as if teleported - into the faster, outer frame, and thus its value inflated by that higher ambient velocity...

[MrVibrating]

Okay, here's something fresh:

For a given RPM, 'edge velocity' of a spinning disc rises with radius.

The outer radii are rotating at exactly the same rate as the inner radii. Same RPM. But there's more matter travelling through more space, the higher the radius gets.

This simple fact could be significant, because it represents a merging of higher and lower-speed reference frames into a single unified system.

To better illustrate my point, we can unfurl the rotating system into a purely linear example:

- suppose we have two 1 kg masses.

- One's flying at an ambient velocity of 1 m/s. Equivalent to our 'inner' mass.

- The other's belting along at 10 m/s. Our 'outer' mass.

- Except these masses are both going in a straight line, not rotating or orbiting..


- Now, apply an impulse between them. So they push off against one another's inertia - being accelerated in opposite directions. Inertia is velocity agnostic so the distribution of momentum from this interaction is equal and opposite.

- because both masses were already moving relative to us, one's been further accelerated, the other, decelerated, from our perspective. So the KE of one has increased, and the KE of the other has decreased.


...and here's the rub - this same identical shot of momentum - fully equitable as it was - is worth different amounts of KE in these two respective reference frames, depending on the respective ambient velocities it applied to.

A 1 kg mass at 1 m/s, then decelerated by 1 m/s, has lost half a Joule of energy.

But a 1 kg mass at 10 m/s, further accelerated up to 11 m/s, has been alloted the same amount of momentum input, but has gained 10 Joules from it.


So hopefully you can now see what i'm looking at; we just roll up our two linear trajectories into a single rotating platform, with a shorter inner path, at lower relative velocity, and a longer outer path, at higher relative velocity.

Remember, that this divergence between these two ambient frames is purely a function of relative radius - so the degree of the prospective thermodynamic asymmetry increases with radius. The bigger the wheel, the bigger the discrepancy between the respective KE values at either radius of this mutual momentum exchange; edge velocity - and thus the magnitude of the asymmetry - rising with the square of radius.

So a simplified test system would seem to be a pair of flywheels with equal MoI's but different radii.

For example, we could have coaxial flywheels - a disc-shaped one, nested inside a ring-shaped one.

Both have equal MoI. And they begin rotating together as one, at equal RPM.

Then a torque is applied between them, accelerating one, while decelerating the other. The momentum deltas will be equal and opposite thanks to CoM and Newton's 3rd, but the RKE changes should vary by the square of relative radius.

The transmission system between the two flywheels is equivalent to a magical transmission that can interconnect masses in two completely different ambient velocity frames - so a mass in a lower-energy frame can effectively 'teleport' its inertial influence into the higher-energy frame, and vice versa, freely hopping between two divergent FoR's, but without having to physically accelerate and decelerate between these two ambient speed frames, as usually enforced by CoM & N3.

In short, a straight radial line drawn across a disc or rotating system, represents a 'tether' between otherwise divergent reference frames. Seriously - trace a straight line from axle to rim.. and you can view that as a kind of effective 'worm hole' through spacetime..

The mechanical implementation needn't be a radially-oriented transmission line - that's just a conceptual metaphor highlighting the deltaV = r^2 gradient, so it could be axially-mounted or whatever - we just need to apply torque between opposing flywheels with identical MoI's but different radii - the greater this difference, the bigger the energy asymmetry..

[MrVibrating]

Here's a baseline standing start:





Will follow up with a rolling start...

[MrVibrating]

Note that we end the baseline with both rotors coasting at 9.548 RPM, in opposite directions.


So, in this next run, we begin at an ambient velocity of 9.548 RPM, this time with all the mass turning in the same direction. As before, though, both masses begin stationary relative to one another, and the same input torque is applied, for the same one second:



Note the difference in final energy compared to the baseline!

Yet we've applied the same torque, to the same inertias, for the same period. So, have we actually input more energy in this second test?

[MrVibrating]

We had a Joule, and we input another, so now we have two Joules, big whoop.

What seems interesting to me though, is that the same torque, inertia and time impulse has two different energies, depending on the starting conditions.

[MrVibrating]

...same again, only this time the sign of the torque's reversed:




At the moment we're just accelerating the reference frames, but what i want to try and do is cause an equal exchange of momentum at unequal orbital velocities, causing an unequal distribution of rising vs falling RKE.

So i'm thinking maybe apply a pair of masses inside each frame, accelerating in opposite directions of rotation, but cross-connected, so that a CW acceleration at wide radius is coupled to a CCW deceleration at lower radius, and vice versa for the other two masses..


Maybe curved scissorjacks or something.. imagine two horizontal jacks, one over the other, then bend 'em both into an arc, so they're at inner and outer radii, and connect the CW-bound outer jack to the CCW-bound inner jack, and vice versa.

Then, the inertias remain balanced on each 'end' of the jack, but each 'end' of the two jacks are at different radii... Something like this:

..


...will have to have a go at knocking something like this up..

[MrVibrating]

Dunno how well i'm explaining myself, but the idea is that the jack will 'feel' equal inertias at each end, although the actual masses at each end are at quite different radii.

The radius of the masses themselves doesn't change, just their angular velocity relative to the net system.

If each of the two jacks, at their respective radii, are experiencing equal CW and CCW inertias, then the net momentum at each radius remains constant, but we have equal and opposite inertias orbiting at different radii, and thus different effective 'edge speed' velocities, and hence KE.

This should yeild an RKE asymmetry from a symmetrical momentum exchange, by my twisted thinking..

[ME]

We had a Joule, and we input another, so now we have two Joules, big whoop.

What seems interesting to me though, is that the same torque, inertia and time impulse has two different energies, depending on the starting conditions.

Energy is an instantaneous conversion factor.

Those discs still have their relative speeds.
Let's say we mount a lightweight baseball bat onto the inner disc, and the outer disc has a baseball (note we could ramp up the weights of those discs to lower the relative losses from this mounting procedure)
In both cases the baseball would be hit with the same relative 19 rpm's (converted to linear speed), and in both cases the baseball would fly away with the same relative speed away from its mounting point.
However from our current frame of reference the final linear speed of the baseball is basically based on the calculated energy.

It's the same baseball-hit-energy but from a different reference point and only brought back to our observing reference point.

[...], by my twisted thinking..

The world would be a boring place if we would all think alike.

[MrVibrating]

Soz if my thinking's a bit muddy - following through differentials in your head is hard - we tend to think in static integrals, which is one reason why the potential prospect of a gravitational asymmetry is so deceptively intuitive and 'accessible'.

Summing over the quasi-static integrals is all the maths and simulation do anyway, but keeping track of inter-related variables, where one's a changing function of another, is simply not something us mere mortals are cut out to do..

If Bessler's solution is a dynamic asymmetry then this is doubtless one reason it's remained so elusive.

Taking the same inductive reasoning to its conclusion, the implication is that a dynamical, emergent asymmetry is precisely what we should be looking for.. something that won't be readily apparent in terms of static integrals..

[MrVibrating]

We had a Joule, and we input another, so now we have two Joules, big whoop.

What seems interesting to me though, is that the same torque, inertia and time impulse has two different energies, depending on the starting conditions.

Energy is an instantaneous conversion factor.

Those discs still have their relative speeds.
Let's say we mount a lightweight baseball bat onto the inner disc, and the outer disc has a baseball (note we could ramp up the weights of those discs to lower the relative losses from this mounting procedure)
In both cases the baseball would be hit with the same relative 19 rpm's (converted to linear speed), and in both cases the baseball would fly away with the same relative speed away from its mounting point.
However from our current frame of reference the final linear speed of the baseball is basically based on the calculated energy.

It's the same baseball-hit-energy but from a different reference point and only brought back to our observing reference point.

Yes, absolutely. All that's being 'input' is work, and decelerating a mass is an output of negative work, even though, internally, it seems identical to an input of positive work.

Everything's symmetrical at the moment, and there's nothing remarkable about transferring momentum. I made a bad choice of words there - what i find interesting here is simply that inertia is velocity agnostic.

The core principle i think i keep coming back to is the notion of equal CW vs CCW momentums, yet posessing unequal energies.

Momentum symmetry, but with RKE asymmetry. So i have this loosely-conceived goal of, EG. dropping a GPE input against the lower-energy angular momentum, while picking up another with the higher-energy equal-opposite angular momentum.

Basically, the notion is that a directional RKE asymmetry is something you can bolt a GPE interaction onto, resulting in an 'effective gravitational asymmetry' - it's not really a gravitational asymmetry, but it looks and behaves like one. However instead of varying effective weight, we're varying the energy values of the momentums against which they're lifted and dropped.

If that makes any sense. But hey, we're obviously looking for something that only just makes sense, when squinted at it in the right light, so it's a fine line eh..

[ME]

what i find interesting here is simply that inertia is velocity agnostic.

That's because Inertia is a lever, it's a measure of how it reacts to applied momentum: a change in momentum.
The Moment of Inertia of an object is basically the sum of all rigidly attached levers for such object where it includes an extra radius component so we can work with angles more easily.

Where a normal lever (balancing scales for instance) acts linearly and a change in momentum is a force through a distance, Inertia shows the rotational variant where a change in momentum is a torque through an angle.

[ME]

what i find interesting here is simply that inertia is velocity agnostic.

That's because Inertia is a lever, it's a measure of how it reacts to applied momentum: a change in momentum.
The Moment of Inertia of an object is basically the sum of all rigidly attached levers for such object where it includes an extra radius component so we can work with angles more easily.

Where a normal [*] change in momentum is a force through a distance, Inertia shows the rotational variant where a change in momentum is a torque through an angle.

[*] edit (deleted some previous nonsense, oops - I think it's better now)

[ruggerodk]

Sliding pendulum pivot

[MrVibrating]

what i find interesting here is simply that inertia is velocity agnostic.

That's because Inertia is a lever, it's a measure of how it reacts to applied momentum: a change in momentum.
The Moment of Inertia of an object is basically the sum of all rigidly attached levers for such object where it includes an extra radius component so we can work with angles more easily.

Where a normal [*] change in momentum is a force through a distance, Inertia shows the rotational variant where a change in momentum is a torque through an angle.

[*] edit (deleted some previous nonsense, oops - I think it's better now)

Totally agree, yep - i'm on no quandry as to the nature of angular inertia; like linear inertia, it is principally a measure of how much mass is being accelerated through a given amount of space, or, equivalently, how much space a given amount of mass is accelerated through: the mass / inertia value being constant, but the radius determining the leverage (i think of it as a power ratio) for a given RPM.

As mentioned previously, if we removed gravity from the Weisenstein / Kassel diagram, then the effective resistance to accelerations felt at the axle is the net compound of all attached inertias - both linear (the stampers and box of bricks) and angular (the pendulums and wheel) - all of that mass is accelerated, in various respective directions, by torquing the axle.

These are all just kickabout ideas for now - i'm convinced the solution's here, somewhere, and have a rough idea of what sort of picture the finished jigsaw will show..


But i do have a nagging conviction that the Kassel / Weissenstein diagrams are using an artifice of historical context regarding the demonstrations, to hide in plain sight a key principal.

[MrVibrating]

Sliding pendulum pivot

Precisely what i've been playing with this evening, and the same game i've played on previous evenings a while back..


This moveable fulcrum is interesting, not least in that it varies the effective distance between the conrod connecting point and the pendulum's axis of rotation.


However in my tests so far, moving the fulcrum just removes energy / GPE.


If the principle does involve moveable fulcrums, then my bet is that this somehow modifies the balance of inertial momentum to counter momentum.

We know, from Adreas Weiss's testimony in "Thorough Report", that the most impressive aspect of the wheel's performance was that it ran at equal speed when raising the 70 lb box of bricks, as when running unloaded.

The wheel in question is the bi-directional model, as shown at Weissenstein, FWIW.

I seem to recall a further testimony relating that the wheel also maintained this constant RPM even when lowering the box of bricks, but can't find that reference right now, so this suggestion is tentative.

But Bessler himself writes that "further mechanical advantage may be gained by the attachment of conventional machinery, such as pumps, mills etc."

This tallies with the aspect that so impressed Weiss. The asymmetry is load matching, at least, up to a point.

This is a powerful clue, and much useful information may be deduced from it.

How and why could a statorless motor produce load-matching torque?

Look at the box of bricks on the right, numbered 22.

If this load is being raised, then follow the rope's direction - it must be being wound onto the axle.

But if the rope is winding onto the axle, raising the box of bricks, then the stampers are being pushed down into the stamping mill..


..or else, more logically, it is the downwards motion of the stampers that is torquing the axle, and thus raising the box of bricks against gravity.

The stampers could either be propelled downwards by gravity, or CF, or both at once.

But if the upper left bearing pivot on the wall bracket does denote a main axis of rotation for the net system, then the downwards motion of the stampers, whatever force propels them, induces a negative torque upon them.

Likewise, whatever raises them back up, doing so produces a positive toque from them.

This question should be bugging Eccentrically1, if not everyone else.. How could the stampers fall upwards again? The diagram doesn't seem to suggest how they could be re-lifted again.

There can't be springs in the stamping box, bouncing them back up again, because all their 'bounce' is sapped on the way down, harnessed, mostly, as torque, of whichever sign.


You can see where i was digging with the flywheels concept, though - stampers fall down under CF, applying torque to the opposing pendulums, via the axle, and these opposing angular momenta, being equal and opposite, produce cancelling counter-inertias, so that the net system momentum remains constant.

Momentum is a function of velocity times inertia, but inertia is not a function of velocity - a mass has equal resistance to accelerations regardless of its current velocity. So, some kind of cyclical inter-reaction between momentum and inertia might be a good place to look for some kind of momentum or KE asymmetry..


I can already see one weakness in my previous approach - the mass sliding out under CF only applied torques (equal and opposite) to the flywheels (pendulums, here - the point is simply that they're opposing angular inertias), whereas in the Weisenstein diagrams the outbound stampers are applying three torques - two opposing ones applied to the pendulums, via a third, in that of the axle and thus main wheel.

In my experiments, the outbound weight only applied negative inertial torque directly to the main wheel, caused by its rising radius as it fell outwards. And then on top of this, it also torqued equal opposing angular inertias.

But that's not what the Weisenstein / Kassel diagrams are showing - the stampers torque the wheel first, which in turn, applies the two opposing torques to the pendulums.

So the key difference here, is that the outbound mass is applying positive torque, to an orbiting axis..


Again, the part the rope is wound around, the axle of the main wheel, is not the main system axis, which instead is the upper left horizontal beam that meets the wall / border. This same central axis of rotation is what the pendulums hang from, suspended radially, outwards. The mechanism here is only dressed to resemble the demonstration apparatus. What it's really showing us is an interesting inertial interaction.


So, people, if the stampers fall out under CF, while applying a torque to the main system, and also two equal opposite counter-torques to the pendulums, such that their counter-inertias cancel, while their counter momentums do not, then what use the moveable fulcrums?


On the diagram featuring an Archimedes screw, the water pump is turned via a square crank wheel. This means the water is raised in fits and starts, accelerating then decelerating on its upwrds course, but also causing fluctuating angular and net system inertia.

The asymmetrically-hung pendulums seem to fulfill mechancially similar purposes to this square wheel, in that their operation is 'notchy' - if we plot the axle's resistance to acceleration across a few cycles it traces a waveform with sharp peaks and troughs.

Is there some analog of moveable fulcrums on the water screw version? Haven't noticed one, yet..

So anyway, we have this varying MoI, self-cancelling counter ineritas, but not necessarily counter-momenta (one's speed invariant, the other speed dependent), we have this load matching property, so the machine is producing more energy, because of the applied load..


There's lines of convergence here. This all comes together, somehow..

If an applied load raises the degree of the interaction's asymmetry, then this tells us somethng about the nature of the asymmetry.

The wheel's own unloaded resistance to accelerations must be the causative principle of the energy asymmetry, and further raising this resistance increases the energy asymetry, up to a point, anyway - Bessler hooked the load up using pulleys and tackle, obviously to keep the load / angle with a beneficial, rather than detrimental, range.

Obviously power = energy * time, which is one obvious reason for not wanting to cause too much slowdown by raising too much weight too fast.

But the proposition is that adding some load, nevertheless raises the degree of excess torque * angle.

If the positive torque is caused by pulling an orbiting mass inwards, then how might varying the resistance to that angular acceleration open up some opportunity?

Similarly, the direct implication (by way of direct illustration, no less) is that an outbound mass, here, causes a positive torque to the net system, first and foremost (the only possible source of torque to raise the box of bricks) - yet it must also undergo angular deceleration as its radial distance increases, so we have an implication that the outbound stampers are inducing both positive and negative torques, and that these are both harnessed differently, sunk into different things; the stampers apply positive torque to the large wheel, and the pendulums, from their CF PE stores. But at the same time, they're applying negative inertial torque to the net system, as they land back in the stamping box.

Could positive torque from an outbound, rather than inbound, mass, provide our load-matching property?

This apparent raising of the efficiency when increasing the resistance to angular accelerations of the net system (such as by applying a load like the box of bricks), could be consistent with an N3 break - as less momentum is accelrated in one direction, so more must be in the other, assuming momentum's conserved, and an asymmetric distribution of momentum is caused, the degree of asymmetry rising with angular resitance of the main system.

Maybe it is angular resistance that draws the masses inwards, inducing positive inertial torques, and somehow rasing the angular resitance causes the masses to be drawn in even further, increasing their radial displacement.

This would imply that, unloaded, the MoI-inducing masses are only using part of their available displacement, which then increases to match the load, until all of the travel is being used.

If, OTOH, the positive torque is OB torque, then braking the wheel must somehow further raise the advantage, until some maximum is reached, beyond which further loading causes a reduction in advantage.

So we have all the elements here of a potential symmetry break; The same sorts of core cencepts we see in MT 80 - 90, of dividing and apportioning and feeding back the forces and inertias in selective ways..

We have the Mendeleev jigsaw, we just need someone to crack the final arrangement.. Post It notes, a wall, some cotton thread, and some ludo, is all we need, i think..


No. 1 question for now, is, how the hell could the stampers fall back up?